A230774 - OEIS

%I #21 Nov 04 2024 17:30:03

%S 1,1,1,1,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,

%T 4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,

%U 5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5

%N Number of primes less than first prime above square root of n.

%C Or repeat k (prime(k)^2 - prime(k-1)^2) times, with prime(0) set to 0 for k = 1.

%C This sequence is useful to compute A055399 for prime numbers.

%H Jean-Christophe Hervé, <a href="/A230774/b230774.txt">Table of n, a(n) for n = 1..10000</a>

%F Repeat 1 prime(1)^2 = 4 times; for k>1, repeat k (prime(k)^2-prime(k-1)^2) = A050216(k-1) times.

%F a(n) - A056811(n) = characteristic function of squares of primes.

%e a(5) = a(6) = a(7) = a(8) = a(9) = 2 because prime(1) = 2 < sqrt(5 to 9) <= prime(2) = 3.

%t Table[1 + PrimePi[Sqrt[n-1]], {n, 100}] (* _Alonso del Arte_, Nov 01 2013 *)

%o (Python)

%o from math import isqrt

%o from sympy import primepi

%o def A230774(n): return primepi(isqrt(n-1))+1 # _Chai Wah Wu_, Nov 04 2024

%Y Cf. A050216, A056811, A055399, A230775.

%K nonn,easy

%O 1,5

%A _Jean-Christophe Hervé_, Nov 01 2013